There are many well-known solid shape data items used to describe solid shapes. “Solid model” and “surface model” among them are used most frequently. The “solid model” means solid shape data structured so that, when a solid body and a point are given, which of the inside, outside, and surface of the solid body includes the point can be determined by a certain procedure. On the other hand, the “surface model” does not have the data structure. A three-dimensional CAD/CAM system usually employs the “solid model”, since the system must determine the mutual interference of solid bodies quickly. For example, the official gazettes of JP-A H8-335279 and JP-A H11-272733 disclose the methods for creating such solid models.
There are also some more well-known methods for creating solid models. The boundary representations (B-reps) is one of those methods. According to this method, vertices, edges, faces and solids are defined algebraically and the mutual topologies are defined so as to describe the target solid shape. The Constructive Solid Geometry (CSG) combines primitives, which are basic elements of a solid shape, thereby describing a complicated solid shape. A three-dimensional bit-map describes a solid shape by defining a grid in a three-dimensional space and it is defined which of the inside, outside, and surface of the three-dimensional space includes each of the areas (cells) divided by the grid.
Each of the above-described methods have merits and defects. Especially, the features of the three-dimensional map are different from those of the B-reps and the CSG. The merits and defects of those methods are as shown below.
The merits of both B-reps and CSG against the three-dimensional bit-map are as follows.                a. Generally, the data size is small.        b. Less calculations are required to process a shape.        c. Feature-related information (part of a shape) is available.        d. Data is exact geometrically.        
The merits of the three-dimensional bit-map against both of B-reps and CSG are as follows:                e. The same data is always assumed for the same shape.        f. The data structure is not affected by slight deformation.        g. The data size is constant even for a complicated shape.        
The defects of both B-reps and CSG against the three-dimensional bit-map are as follows:                e. The same data is not always assumed for the same shape.        f. The data structure might be changed significantly by slight deformation.        g. The data size is limitless for a complicated shape.        
The defects of the 3-dimensional bit-map against both B-reps and CSG are as follows:                a. The data size usually becomes large.        b. Many calculations are required to process a shape.        c. No feature-related information (geometrical properties of a shape) is available.        d. Data is not so accurate geometrically. Translation is needed depending on the subject model.        
For how to describe a solid model and the features of each of the methods, refer to the documents as “Computer Graphics” (J. D. Foley, A. Dam, S. K. Feiner, J. F. Hughes/Addition-Wesley Inc.), etc.
In any of the conventional 3-dimensional CAD systems, B-reps and CSG have been used for solid models. In recent years, however, the merits of the three-dimensional bit-map come to be recognized once again now that the computer performance has been improved significantly, free shape processing have become easier, free from designing has become possible, designs are of great account, and reverse engineering that creates solid shape data by measuring natural things and existing products has become wide-spread. Using such 3-dimensional bit-maps for designing a solid shape, therefore, enables a comparison to be made among a plurality of shapes, optimize a shape by repeating slight deformation for it, and record a real body as data through 3-dimensional measurements without requiring any special technique.
While a 3-dimensional bit-map has the above described (a to d) defects, the defects b and d are almost solved by the rapid progress of the computer processing ability. The defects a and c, however, have still remained as unsolved problems.
A data compression technique may be used to reduce the data size. Complicated data compression by the LZ method or the like, however, should be avoided, since the whole subject solid model data must be extended each time it is used. This makes it difficult to use the solid model. This is why there has been no choice for data compression but using a comparatively simple and partial data compression method such as the oct-tree method. Improvement of the compression rate has been difficult so far.
To provide a solid shape with feature-related information, for example, geometrical characteristics, as well as meaning, machining method, and accuracy of the solid shape, a method for adding solid shape data described using the B-reps and CSG methods to the subject solid shape has been used sometimes. This method, however, increases the data size and almost lose the merits e, f, and g of the 3-dimensional bit-map.
Any of the above conventional techniques, therefore, have not so effective to solve the defects of the 3-dimensional bit-map while the merits thereof are kept as are.